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Uniqueness of gravitational constant at low energies from the connection between spin-2 and spin-0 sectors

Duojie Jimu, Tomislav Prokopec

Abstract

The fact that graviton propagator contains not only one but two tensorial components excludes a unique definition of the running behavior of the gravitational constant, while at low energies gravitation is characterized solely by Newton's constant. How these two facts are reconciled when massive quantum fields are present remains unanswered. In this work, by non-minimally coupling gravity to a one-loop massive scalar, we show that this potential conflict is resolved by the non-trivial equivalence between the residues of the two propagator components. Such equivalence, crucial for the validity of the Appelquist-Carazzone decoupling theorem, is based on a rather subtle connection between the spin-2 and spin-0 sectors of the propagator. It is verified that this connection also makes the two quantum-corrected gravitational potentials be characterized by the same gravitational constant at large distances. In addition, we find that the potentials in our case as well as the quantum-corrected Coulomb potential can be expressed concisely in a unified formulation. By comparing these results with experiments, we establish a new upper bound on the magnitude of the non-minimal coupling parameter $ξ$.

Uniqueness of gravitational constant at low energies from the connection between spin-2 and spin-0 sectors

Abstract

The fact that graviton propagator contains not only one but two tensorial components excludes a unique definition of the running behavior of the gravitational constant, while at low energies gravitation is characterized solely by Newton's constant. How these two facts are reconciled when massive quantum fields are present remains unanswered. In this work, by non-minimally coupling gravity to a one-loop massive scalar, we show that this potential conflict is resolved by the non-trivial equivalence between the residues of the two propagator components. Such equivalence, crucial for the validity of the Appelquist-Carazzone decoupling theorem, is based on a rather subtle connection between the spin-2 and spin-0 sectors of the propagator. It is verified that this connection also makes the two quantum-corrected gravitational potentials be characterized by the same gravitational constant at large distances. In addition, we find that the potentials in our case as well as the quantum-corrected Coulomb potential can be expressed concisely in a unified formulation. By comparing these results with experiments, we establish a new upper bound on the magnitude of the non-minimal coupling parameter .
Paper Structure (15 sections, 80 equations, 4 figures)

This paper contains 15 sections, 80 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preparation: deriving the dressed graviton propagator
  3. Manifestly transverse self-energy
  4. Resumming diagrams
  5. The spin-2 and spin-0 residues match up
  6. Preparation: deriving the quantum-corrected gravitational potentials
  7. Solving the effective field equations
  8. Corrections to the two potentials converge at large distances
  9. Properties of the gravitational potentials in position space
  10. Setting up the on-shell scheme
  11. Unified formulation for gravitational and Coulomb potentials
  12. Experimental constraint
  13. Discussion
  14. Feynman rules and amplitudes
  15. Integrals

Figures (4)

  • Figure 1: The dressed propagator given by a summation over the bubble diagrams with increasing number of self-energy insertions.
  • Figure 2: Feynman diagrams contributing to the graviton self-energy. Coiled lines and solid lines represent graviton and the scalar, respectively.
  • Figure 3: The contour used to evaluate the $n=2$ case of \ref{['contour_integral']}. It comprises eight pieces and bypasses both the branch cut along the imaginary line and the pole at the origin. $\gamma_{2}$ and $\gamma_{6}$ are infinitesimal semicircles. When $n=0$ or $n=1$, there's no pole at the origin so we do not need to curve the contour like $\gamma_{2}$.
  • Figure :